{"id":24632,"date":"2023-04-01T10:48:39","date_gmt":"2023-04-01T09:48:39","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=24632"},"modified":"2023-04-01T15:24:36","modified_gmt":"2023-04-01T14:24:36","slug":"qual-e-o-conjunto-solucao-de-cada-uma-das-equacoes","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=24632","title":{"rendered":"Resolve as seguintes equa\u00e7\u00f5es"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_24632' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_24632' class='GTTabs_curr'><a  id=\"24632_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_24632' ><a  id=\"24632_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_24632'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Resolve as seguintes equa\u00e7\u00f5es.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 160px;\">\n<tbody>\n<tr style=\"height: 20px;\">\n<td style=\"width: 3.125%; height: 20px;\">a)<\/td>\n<td style=\"text-align: left; width: 96.7449%; height: 20px;\">\\(4{x^2} &#8211; 49 = 0\\)<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 3.125%; height: 20px;\">b)<\/td>\n<td style=\"text-align: left; width: 96.7449%; height: 20px;\">\\(2{x^2} &#8211; 50 = 0\\)<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 3.125%; height: 20px;\">c)<\/td>\n<td style=\"text-align: left; width: 96.7449%; height: 20px;\">\\({\\left( {x + 4} \\right)^2} &#8211; 9 = 0\\)<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 3.125%; height: 20px;\">d)<\/td>\n<td style=\"text-align: left; width: 96.7449%; height: 20px;\">\\({\\left( {x &#8211; 3} \\right)^2} + 4 = 0\\)<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 3.125%; height: 20px;\">e)<\/td>\n<td style=\"text-align: left; width: 96.7449%; height: 20px;\">\\(3{x^2} + 4 = {x^2} + 4\\)<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 3.125%; height: 20px;\">f)<\/td>\n<td style=\"text-align: left; width: 96.7449%; height: 20px;\">\\(4{x^2} &#8211; {\\left( {x + 1} \\right)^2} = 0\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_24632' onClick='GTTabs_show(1,24632)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_24632'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>As equa\u00e7\u00f5es est\u00e3o resolvidas abaixo.<\/p>\n<table style=\"border-collapse: collapse;\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td style=\"text-align: left;\">\\(4{x^2} &#8211; 49 = 0\\)<\/td>\n<td style=\"text-align: left;\">\\[\\begin{array}{*{20}{l}}{4{x^2} &#8211; 49 = 0}&amp; \\Leftrightarrow &amp;{4{x^2} = 49}\\\\{}&amp; \\Leftrightarrow &amp;{{x^2} = \\frac{{49}}{4}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = &#8211; \\sqrt {\\frac{{49}}{4}} }&amp; \\vee &amp;{x = + \\sqrt {\\frac{{49}}{4}} }\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = &#8211; \\frac{7}{2}}&amp; \\vee &amp;{x = \\frac{7}{2}}\\end{array}}\\end{array}\\]<\/td>\n<\/tr>\n<tr>\n<td>b)<\/td>\n<td style=\"text-align: left;\">\\(2{x^2} &#8211; 50 = 0\\)<\/td>\n<td style=\"text-align: left;\">\\[\\begin{array}{*{20}{l}}{2{x^2} &#8211; 50 = 0}&amp; \\Leftrightarrow &amp;{2{x^2} = 50}\\\\{}&amp; \\Leftrightarrow &amp;{{x^2} = 25}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = &#8211; 5}&amp; \\vee &amp;{x = 5}\\end{array}}\\end{array}\\]<\/td>\n<\/tr>\n<tr>\n<td>c)<\/td>\n<td style=\"text-align: left;\">\\({\\left( {x + 4} \\right)^2} &#8211; 9 = 0\\)<\/td>\n<td style=\"text-align: left;\">\\[\\begin{array}{*{20}{l}}{{{\\left( {x + 4} \\right)}^2} &#8211; 9 = 0}&amp; \\Leftrightarrow &amp;{{{\\left( {x + 4} \\right)}^2} = 9}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x + 4 = &#8211; 3}&amp; \\vee &amp;{x + 4 = + 3}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = &#8211; 7}&amp; \\vee &amp;{x = &#8211; 1}\\end{array}}\\end{array}\\]<\/td>\n<\/tr>\n<tr>\n<td>d)<\/td>\n<td style=\"text-align: left;\">\\({\\left( {x &#8211; 3} \\right)^2} + 4 = 0\\)<\/td>\n<td style=\"text-align: left;\">\\[\\begin{array}{*{20}{l}}{{{\\left( {x &#8211; 3} \\right)}^2} + 4 = 0}&amp; \\Leftrightarrow &amp;{{{\\left( {x &#8211; 3} \\right)}^2} = &#8211; 4}\\\\{}&amp; \\Leftrightarrow &amp;{x \\in \\emptyset }\\end{array}\\]<\/td>\n<\/tr>\n<tr>\n<td>e)<\/td>\n<td style=\"text-align: left;\">\\(3{x^2} + 4 = {x^2} + 4\\)<\/td>\n<td style=\"text-align: left;\">\\[\\begin{array}{*{20}{l}}{3{x^2} + 4 = {x^2} + 4}&amp; \\Leftrightarrow &amp;{2{x^2} = 0}\\\\{}&amp; \\Leftrightarrow &amp;{{x^2} = 0}\\\\{}&amp; \\Leftrightarrow &amp;{x = 0}\\end{array}\\]<\/td>\n<\/tr>\n<tr>\n<td>f)<\/td>\n<td style=\"text-align: left;\">\\(4{x^2} &#8211; {\\left( {x + 1} \\right)^2} = 0\\)<\/td>\n<td style=\"text-align: left;\">\\[\\begin{array}{*{20}{l}}{4{x^2} &#8211; {{\\left( {x + 1} \\right)}^2} = 0}&amp; \\Leftrightarrow &amp;{{{\\left( {2x} \\right)}^2} &#8211; {{\\left( {x + 1} \\right)}^2} = 0}\\\\{}&amp; \\Leftrightarrow &amp;{\\left( {2x + \\left( {x + 1} \\right)} \\right)\\left( {2x &#8211; \\left( {x + 1} \\right)} \\right) = 0}\\\\{}&amp; \\Leftrightarrow &amp;{\\left( {3x + 1} \\right)\\left( {x &#8211; 1} \\right) = 0}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{3x + 1 = 0}&amp; \\vee &amp;{x &#8211; 1 = 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = &#8211; \\frac{1}{3}}&amp; \\vee &amp;{x = 1}\\end{array}}\\end{array}\\]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<\/p>\n<h6 class=\"fittexted_for_content_h6\">ALTERNATIVA PARA A RESOLU\u00c7\u00c3O DA EQUA\u00c7\u00c3O<\/h6>\n<p>Vamos resolver seguidamente as tr\u00eas primeiras equa\u00e7\u00f5es utilizando um processo diferente.<\/p>\n<p>\u00a0<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{4{x^2} &#8211; 49 = 0}&amp; \\Leftrightarrow &amp;{\\left( {2x + 7} \\right)\\left( {2x &#8211; 7} \\right) = 0}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{2x + 7 = 0}&amp; \\vee &amp;{2x &#8211; 7 = 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = &#8211; \\frac{7}{2}}&amp; \\vee &amp;{x = \\frac{7}{2}}\\end{array}}\\end{array}\\]<\/p>\n<p>\u00a0<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{2{x^2} &#8211; 50 = 0}&amp; \\Leftrightarrow &amp;{{x^2} &#8211; 25 = 0}\\\\{}&amp; \\Leftrightarrow &amp;{\\left( {x + 5} \\right)\\left( {x &#8211; 5} \\right) = 0}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x + 5 = 0}&amp; \\vee &amp;{x &#8211; 5 = 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = &#8211; 5}&amp; \\vee &amp;{x = 5}\\end{array}}\\end{array}\\]<\/p>\n<p>\u00a0<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{{\\left( {x + 4} \\right)}^2} &#8211; 9 = 0}&amp; \\Leftrightarrow &amp;{{{\\left( {x + 4} \\right)}^2} &#8211; {3^2} = 0}\\\\{}&amp; \\Leftrightarrow &amp;{\\left( {\\left( {x + 4} \\right) + 3} \\right)\\left( {\\left( {x + 4} \\right) &#8211; 3} \\right) = 0}\\\\{}&amp; \\Leftrightarrow &amp;{\\left( {x + 7} \\right)\\left( {x + 1} \\right) = 0}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x + 7 = 0}&amp; \\vee &amp;{x + 1 = 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = &#8211; 7}&amp; \\vee &amp;{x = &#8211; 1}\\end{array}}\\end{array}\\]<\/p>\n<p>\u00a0<\/p>\n<p>Em que consistiu o processo diferente usado na resolu\u00e7\u00e3o destas tr\u00eas equa\u00e7\u00f5es?<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_24632' onClick='GTTabs_show(0,24632)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Resolve as seguintes equa\u00e7\u00f5es. a) \\(4{x^2} &#8211; 49 = 0\\) b) \\(2{x^2} &#8211; 50 = 0\\) c) \\({\\left( {x + 4} \\right)^2} &#8211; 9 = 0\\) d) \\({\\left( {x &#8211; 3}&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14061,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[100,97,700],"tags":[424,706,198],"series":[],"class_list":["post-24632","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-monomios-e-polinomios","tag-8-o-ano","tag-equacao-incompleta-do-2-o-grau","tag-lei-do-anulamento-do-produto"],"views":102,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat06.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24632","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=24632"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24632\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24632"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24632"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24632"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=24632"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}